To avoid generating an undesirably large set of frequent itemsets for discovering all high confidence association rules, the problem of finding frequent closed itemsets in a formal mining context is proposed. In this paper, aiming to these shortcomings of typical algorithms for mining frequent closed itemsets, such as the algorithm A-close and CLOSET, we propose an efficient algorithm for mining frequent closed itemsets, which is based on Galois connection and granular computing. Firstly, we present the smallest frequent closed itemsets and its characters, contain some properties and theorems, then propose a novel notion, called the smallest frequent closed granule, which can help the algorithm save reading the database to reduce the costed I/O for discovering frequent closed itemsets. And then we propose a novel model for mining frequent closed itemsets based on the smallest frequent closed granules, and a connection function for generating the smallest frequent closed itemsets. The generator function create the power set of the smallest frequent closed itemsets in the enlarged frequent 1-item manner, which can efficiently avoid generating an undesirably large set of candidate smallest frequent closed itemsets to reduce the costed CPU and the occupied main memory for generating the smallest frequent closed granules. Finally, we describe the algorithm for the proposed model. On these different datasets, we report the performances of the algorithm and its trend of the performances to discover frequent closed itemsets, and further discuss how to solve the bottleneck of the algorithm. For mining frequent closed itemsets, all these experimental results indicate that the performances of the algorithm are better than the traditional and typical algorithms, and it also has a good scalability. It is suitable for mining dynamic transactions datasets.